72 MOTION OF A SPINNING BODY
suppose that at a certain latitude, the angular velocity of the gyroaxle relative to the earth, about a vertical axis, is w radians per second. Then motion of the gyro-axle in azimuth can be prevented by the application of a torque about the east-west axis that will produce a precessional velocity wp = w, given by the Second Law of Gyrodynamics:
L = w K3w3
where L is the torque expressed in pound-feet, KS is the moment of inertia of the gyro relative to the spin-axle expressed in slugfeet', and w3 is the spin-velocity expressed in radians per second.
If angular velocity of the spin-axle relative to the earth expressed in degrees per minute of time be represented by w', moment of inertia of the gyro relative to the spin-axle expressed in pound-feet2 be represented by KS', and spin-velocity expressed in revolutions per minute be represented by n, then the above equation may be written
L[= W/ KS' 2 an = 0.00000095 w' K3'n (66)
wKsws = (57.3)60 32.1 60
The vertical component, relative to the earth, of the angular velocity of the spin-axle of a freely suspended gyro in latitude X is
W = we sin X (68)
where we represents the angular velocity of the earth about the geographic axis.
Since the angular velocity of the earth is [360° = 24 X 601 _ 0.25° per minute of time,
w' = 0.25 sin X degrees per minute of time. (69)
42. The Sperry Directional Gyro. - The indications of a magnetic compass on an airplane can be relied upon only when the airplane is steady and moving in a straight course with constant speed. In taking a compass reading, the common practice is to steady the airplane in a straight course when near the desired compass heading and wait till the oscillations of the needle have become sufficiently small. To maintain a straight course either the ground must be visible or some gyroscopic turn-indicator must be available.
The various uncertainties in the indications of the magnetic compass have caused it to be largely displaced by the gyro-compass for naviaatina rn;rrine vessels, but the considerable weieht